1. The problem statement, all variables and given/known data Show that: (|x+y|)/(1+|x+y|) ≤ ((|x|)/(1+|x|)) + ((|y|)/(1+|y|)) 2. Relevant equations You are given the triangle inequality: |x+y| ≤ |x| + |y| 3. The attempt at a solution (This is done from the result, as I haven't been able to find the starting point) (|x+y|)/(1+|x+y|) ≤ (|x|(1+|y|)+|y|(1+|x|))/((1+|x|)(1+|y|)) (|x+y|)/(1+|x+y|) ≤ (|x|+2|x||y|+|y|)/(1+|x|+|y|+|x||y|) This doesn't seem to go anywhere. I also tried flipping the whole thing to get: (1+|x+y|)/(|x+y|)≤(1+|x|)/(|x|)+(1+|y|)/(|y|) but this doesn't seem to lead anywhere either... I'm not sure how to go about this problem.